
Introduction  Preview Material  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2006; 319 pp; hardcover Volume: 76 ISBN10: 0821841807 ISBN13: 9780821841808 List Price: US$61 Member Price: US$48.80 Order Code: GSM/76 See also: An Introduction to Measure Theory  Terence Tao A First Course in Sobolev Spaces  Giovanni Leoni A (Terse) Introduction to Lebesgue Integration  John Franks Introduction to Differential Equations  Michael E Taylor  This selfcontained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to \(L^p\) spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to \(L^2\) spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on \(n\)dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory. Request an examination or desk copy. Readership Graduate students interested in analysis. Reviews "Taylor's treatment throughout is elegant and very efficient ... I found reading the text very enjoyable."  MAA Reviews "The book is very understandable, requiring only a basic knowledge of analysis. It can be warmly recommended to a broad spectrum of readers, to graduate students as well as young researchers."  EMS Newsletter "This monograph provides a quite comprehensive presentation of measure and integration theory and of some of their applications."  Mathematical Reviews 


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